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A preconditioner defined by an algebraic multigrid cycle for a damped Helm-holtz operator is proposed for the Helmholtz equation. This approach is well-suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the precondi-tioned systems and the convergence of the GMRES(More)
Efficient numerical methods for pricing American options using Heston's stochastic volatility model is proposed. Based on this model the price of a Eu-ropean option can be obtained by solving a two-dimensional parabolic partial differential equation. For an American option the early exercise possibility leads to a lower bound for the price of the option.(More)
A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The rst objective function is the drag coeecient. As a constraint, it is required that the lift coeecient is above a given value. The CFD(More)
The deterministic numerical valuation of American options under Heston's stochastic volatility model is considered. The prices are given by a linear com-plementarity problem with a two-dimensional parabolic partial differential operator. A new truncation of the domain is described for small asset values while for large asset values and variance a standard(More)
Stochastic volatility models lead to more realistic option prices than the Black-Scholes model which uses a constant volatility. Based on such models a two-dimensional parabolic partial differential equation can derived for option prices. Due to the early exercise possibility of American option contracts the arising pricing problems are free boundary(More)